This map indicates Mackenzie's route to the Arctic Ocean in 1789 (marked in red), and his route to the Pacific Ocean in 1793 (marked in yellow). The section shown here traces Mackenzie's routes in northwestern Canada, and doesn't include the entire route from point of origin (Montreal).
Map source: Voyages from Montreal on the river St. Laurence through the continent of North America to the frozen and Pacific Oceans, in the years 1789 and 1793. London: T. Cadell, J. and W. Davies, 1801.